CN109188687A - A method of the same focal spot array of two dimension is generated using the radiation field of planar array antenna - Google Patents
A method of the same focal spot array of two dimension is generated using the radiation field of planar array antenna Download PDFInfo
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- CN109188687A CN109188687A CN201811246310.6A CN201811246310A CN109188687A CN 109188687 A CN109188687 A CN 109188687A CN 201811246310 A CN201811246310 A CN 201811246310A CN 109188687 A CN109188687 A CN 109188687A
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Abstract
The present invention relates to a kind of method that the radiation field using planar array antenna generates the same focal spot array of two dimension, the present invention uses two high numerical aperture lens to form 4 π focusing systems first；Then in the one virtual planar array antenna of focal plane central array for 4 π focusing systems being made of two high numerical aperture lens；The electromagnetic field of antenna array radiation propagates the lens for reaching image space side outward, and is collected completely by two high numerical aperture lens, then continues to travel on the pupil plane of two lens, obtains the field distribution on pupil plane；The field distribution on pupil plane is finally considered as in-field and is inversely transferred to Jiao Qu, the same focal spot array of two dimension with predetermined properties is generated on the focal plane of high numerical aperture lens.The present invention generates the same focal spot array of two dimension with predetermined quantity, spacing and position using the method without optimization.
Description
Technical field
The present invention relates to the generation technology field of two-dimentional focal spot array, especially a kind of radiation field using planar array antenna
The method for generating the same focal spot array of two dimension.
Background technique
It is widely studied by the sub-wavelength focal spot generated under high-NA (NA) lens tightly focused, because it is in optics
Microscope, optical tweezer, photon capture have important application with manipulation, single molecular fluorescence spectrum etc..In addition, certain parallel and
The specific occasion of synchronization process needs the two-dimentional focal spot array an of controlled properties.Therefore, many to create two-dimentional focal spot arrays
Method is suggested.
In 2000, D.Fittinghoff et al. propose using the method for cascade beam splitter generate one 8 × 2 when
Between irrelevant focal spot array.2011, H.Guo et al. utilization was made of two orthogonal polarized light beams that non-uniform polarisation is modulated
Compound vector light beam controls number of focal spots and main polarization field.2013, M.Cai et al. was demonstrated in numerical value and experimentally by tying
The generation and adjusting of the multifocal spot of sub-wavelength after structure vectorial field tightly focused；The same year, J.Bar-David et al. propose a kind of generation
The method of radial polarisation phasmon focal spot periodic array.2014, L.Zhu et al. proposed a kind of at the back aperture of lens
The method that phase-only modulation realizes multifocal spot array is carried out using point shape Talbor effect of special designing；The same year,
K.Prabakaran et al. advises, and Bessel-Gauss beams is passed through multiple phase filtering, then tight with high numerical aperture lens
After focusing, multistage sub-wavelength focal spot can be generated.2015, D.Zhang et al. proposed a kind of utilization radial polarisation Bezier-
Gaussian beam constructs the multifocal lattice array of position and polarization direction controllably.
Above-mentioned reported method usually requires optimization design optical element, so that optimum efficiency be not achieved.In addition, above-mentioned
Focal spot intensity distribution in array caused by method is not uniform enough, and the quantity of focal spot and position are not easy to manipulate.In order to overcome
The limitation of the above method, we have proposed a kind of methods without optimization to generate with predetermined quantity, spacing and position
The same focal spot array of two dimension.
Summary of the invention
In view of this, the purpose of the present invention is to propose to a kind of radiation fields using planar array antenna to generate the same focal spot of two dimension
The method of array generates the same focal spot array of two dimension with predetermined quantity, spacing and position using the method without optimization.
The present invention is realized using following scheme: a kind of same focal spot array of radiation field generation two dimension using planar array antenna
Method, comprising the following steps:
Step S1: 4 π focusing systems are formed using two high numerical aperture lens；
Step S2: in the focal plane (XY for the 4 π focusing systems of step S1 being made of two high-NA (NA) lens
Plane) one virtual planar array antenna of central array；The electric field of antenna array radiationIt propagates and is reached as empty outward
Between side lens, and collected completely by two high numerical aperture lens, then continue to the pupil plane for traveling to two lens
On, obtain the field distribution on pupil planeWherein,It is spherical coordinates,It is the polar coordinates on pupil plane, θ
Indicate the angle between radiation direction and Z axis (optical axis),Indicate azimuth, ρ indicates polar diameter；
Step S3: by the field distribution on the pupil plane in step S2It is considered as in-field and is inversely transferred to coke
Area generates the same focal spot array of two dimension with predetermined properties on the focal plane of high numerical aperture lens.
Further, in step S2, the electric field of the antenna array radiationIt is indicated using following formula:
In formula, C0It is the coefficient unrelated with antenna pattern,It is the unit vector along the direction θ,It is first factor,It is array factor；For electric Hertz antenna unit,
Projection function g (θ) and apodizing function P (θ) for deferring to the lens of Helmholtz's condition, in spheric wave front
Are as follows:
G (θ)=tan θ；
The then field distribution on pupil planeIt is calculated by following formula:
In formula,Indicate azimuth,Indicate the unit vector of X-direction,Indicate the unit vector of Y direction.
Further, if planar array antenna is the M × N number of unit rectangle battle array arranged along X-axis and Y-axis, battle array
The factorIt indicates are as follows:
In formula, k=2 π/λ is wave number, dxAnd dyRespectively represent row and column spacing of the adjacent element between X-axis and Y-axis, M
Indicate that the element number of array arranged along X-axis, N indicate the element number of array arranged along Y-axis；
If planar array antenna is circle made of circumferentially arranging, array factorIt indicates are as follows:
In formula, R indicates that the radius of circular array, Q indicate the element number of array circumferentially arranged,It is the side of q-th of array element
Parallactic angle.
Further, in step S3, the Field distribution of focal plane on focal plane are as follows:
In formula,φ=cos-1(x/r), C1It is amplitude constant, Ex(r,φ,z)、Ey(r, φ, z) and Ez
(r, φ, z) is illustrated respectively in X, Y, Z-direction field component at point of observation on focal plane (r, φ, z=0).
Compared with prior art, the invention has the following beneficial effects: the present invention is generated using the radiation field of planar array antenna
Interminable iterative optimization procedure is not necessarily to when two-dimentional same focal spot array, and each focal spot shape is identical with intensity, controllable quantity, position
It sets and is spaced and is customizable.
Detailed description of the invention
Fig. 1 (a) is 4 π focusing structures of the embodiment of the present invention, wherein planar array antenna is with two high-NAs (NA)
It is placed centered on the focus of lens along X/Y plane.
Fig. 1 (b) is the square-shaped array schematic diagram of the embodiment of the present invention being made of M × N number of array element.
Fig. 1 (c) is the circular array schematic diagram as made of Q array element arrangement of the embodiment of the present invention.
Fig. 2 is the rectangle focusspot array of the embodiment of the present invention.In Fig. 2, (a) is 2 × 3 focal spot arrays, (b) is 3 × 2 focal spots
Array (c) is 3 × 3 focal spot arrays.
Fig. 3 is the diagonal line focal spot array of the embodiment of the present invention.In Fig. 3, (a) is right diagonal line focal spot array, is (b) left side
Diagonal line focal spot array (c) is V-arrangement focal spot array.
Fig. 4 is the regular polygon focal spot array of the embodiment of the present invention.In Fig. 4, (a) is regular pentagon focal spot array, (b) is
Regular hexagon focal spot array (c) is octagon focal spot array.
Fig. 5 is the round focal spot array of the embodiment of the present invention.In Fig. 5, respectively along radius R=3 λ, the circumference of 3.5 λ and 4 λ
(a) uniform six focal spots array of arrangement, (b) uniform eight focal spots array, and (c) non-homogeneous eight focal spots array.
Fig. 6 is the embodiment of the present invention on normalization pupil plane, generates uniform eight focal spots circular array (see Fig. 5 (b))
Required normalization incidence field distribution.
Specific embodiment
The present invention will be further described with reference to the accompanying drawings and embodiments.
It is noted that described further below be all exemplary, it is intended to provide further instruction to the application.Unless another
It indicates, all technical and scientific terms used herein has usual with the application person of an ordinary skill in the technical field
The identical meanings of understanding.
It should be noted that term used herein above is merely to describe specific embodiment, and be not intended to restricted root
According to the illustrative embodiments of the application.As used herein, unless the context clearly indicates otherwise, otherwise singular
Also it is intended to include plural form, additionally, it should be understood that, when in the present specification using term "comprising" and/or " packet
Include " when, indicate existing characteristics, step, operation, device, component and/or their combination.
Present embodiments provide a kind of method that the radiation field using planar array antenna generates the same focal spot array of two dimension, packet
Include following steps:
Step S1: 4 π focusing systems are formed using two high numerical aperture lens (NA)；
Step S2: in the focal plane (XY for the 4 π focusing systems of step S1 being made of two high-NA (NA) lens
Plane) one virtual planar array antenna of central array, as shown in Fig. 1 (a)；The electric field of antenna array radiationOutward
The lens for reaching image space side are propagated, and are collected completely by two high numerical aperture lens, then continue to travel to two
On the pupil plane of lens, the field distribution on pupil plane is obtainedWherein,It is spherical coordinates,It is pupil plane
On polar coordinates, θ indicates the angle between radiation direction and Z axis (optical axis),Indicate azimuth, ρ indicates polar diameter；
Step S3: by the field distribution on the pupil plane in step S2It is considered as in-field and is inversely transferred to coke
Area generates the same focal spot array of two dimension with predetermined properties on the focal plane of high numerical aperture lens.
In the present embodiment, in step S2, according to directional diagram product principle, the electric field of the antenna array radiation
It is indicated using following formula:
In formula, C0It is the coefficient unrelated with antenna pattern,It is the unit vector along the direction θ,It is first factor,It is array factor；For electric Hertz antenna unit,
Projection function g (θ) and apodizing function P (θ) for deferring to the lens of Helmholtz's condition, in spheric wave front
Are as follows:
G (θ)=tan θ；
The then field distribution on pupil planeIt is calculated by following formula:
In formula,Indicate azimuth,Indicate the unit vector of X-direction,Indicate the unit vector of Y direction.
In the present embodiment, if planar array antenna is the M × N number of unit rectangle battle array arranged along X-axis and Y-axis,
As shown in Fig. 1 (b), then array factorIt indicates are as follows:
In formula, k=2 π/λ is wave number, dxAnd dyRespectively represent row and column spacing of the adjacent element between X-axis and Y-axis, M
Indicate that the element number of array arranged along X-axis, N indicate the element number of array arranged along Y-axis；Array grid (or lattice) can have equal
Or unequal row and column spacing.
If planar array antenna is circle made of circumferentially arranging, as shown in Fig. 1 (c), then array factor
It indicates are as follows:
In formula, R indicates that the radius of circular array, Q indicate the element number of array circumferentially arranged,It is the side of q-th of array element
Parallactic angle.
In the present embodiment, in step S3, using Richards-Wolf vector diffraction integral formula, focal plane is calculated
On Field distribution of focal plane are as follows:
In formula,φ=cos-1(x/r), C1It is amplitude constant, Ex(r,φ,z)、Ey(r, φ, z) and Ez
(r, φ, z) is illustrated respectively in X, Y, Z-direction field component at point of observation on focal plane (r, φ, z=0).So far, the present embodiment can
To be located at the controllable focal spot array of the two dimension on focal plane using above-mentioned formula building.
Embodiment one.
Coefficient C0And C1Because unrelated with the focal spot shapes in array, 1 is normalized in order to simplify.It is radiated from antenna array
Pupil plane should be collected completely and be collimated in field, for constructing focal spot array.Therefore, the greatest irradiation angle of lens is set as θmax=
Pi/2, corresponding numerical aperture NA=1, the value can be reached by using reflection lens or hyperplane lens.Here it provides
Four kinds of different types of specific focal spot arrays, the simplicity and flexibility of method are proposed with proving institute.Respectively by 2 × 3,3 × 2,3
× 3 array elements, are separated by dx=2.5 λ and dy=5.0 λ, dx=5.0 λ and dy=2.5 λ, dx=2.5 λ and dy=2.5 λ, arrange
Dipole rectangle battle array (including rectangular battle array) radiation field for generating the same focal spot array of two dimension, as shown in Figure 2.From Fig. 2
It can be clearly seen that the focal spot on focal plane is corresponded with the dipole in rectangle battle array, and each focal spot is having the same
Intensity and volume.In addition, two adjacent focal spots are along the spacing of X-axis and Y-axis only by dxAnd dyValue determines, and is approximately equal to dxWith
dyValue.In Fig. 2, (a) is 2 × 3 focal spot arrays, (b) is 3 × 2 focal spot arrays, (c) is 3 × 3 focal spot arrays.
Embodiment two.
If five dipole antennas diagonally arrange, it is divided into dx=1.5 λ and dy=1.5 λ, by its radiation direction
Figure, generates diagonal focal spot array, as shown in Figure 3 in which can be convenient on XY focal plane.Similarly, the intensity of each focal spot is identical
, and its center can be by adjusting parameter dxAnd dyTo customize.In Fig. 3, (a) is right diagonal line focal spot array, (b)
It (c) is V-arrangement focal spot array for left diagonal line focal spot array.
Embodiment three.
Fig. 4 shows regular pentagon, regular hexagon and octagon focal spot array.The distribution of these regular polygon focal spots is held very much
Easily realized by the radiation field using the antenna array with regular pentagon, regular hexagon and octagon arrangement.Obviously, may be used
To use this method to generate other polygon focal spot arrays.This shows that required polygon focal spot array can be by inverting phase
The radiation field for the polygon Dipole Arrays answered obtains, and the center of each focal spot can be by adjusting phase on XY focal plane
The dipole array element coordinate answered manipulates.In Fig. 4, (a) is regular pentagon focal spot array, (b) is regular hexagon focal spot array,
It (c) is octagon focal spot array.
Example IV.
Round focal spot array is generated using circular dipole array.Fig. 5 (a), 5 (b) and 5 (c) are showed respectively along radius R
Uniform six focal spots, uniform eight focal spot and non-homogeneous eight focal spot of the circumference of=3 λ, R=3.5 λ and R=4 λ arrangement.It can be found that
The radius of a circle and focal spot position of focal spot array can be respectively by formulaIt gives
Parameter R out andEasily control.In addition, the focal spot number in array is equal to parameter value Q.It is respectively along radius R=in Fig. 5
The uniform six focal spots array of (a) of the circumferential arrangement of 3 λ, 3.5 λ and 4 λ, (b) uniform eight focal spots array, and (c) non-homogeneous eight focal spot
Array.
On normalization pupil plane, for incident field distribution needed for generating the same focal spot array of two dimensionIt can be with
From formulaIt is calculated.As an example, Fig. 6 depicts wound
Normalization incidence field mode needed for building uniform eight focal spots circular array shown in Fig. 5 (b).It can be with clear view to entering from Fig. 6
The radial polarisation field that field is spatial modulation is penetrated, there are eight cyclic pattern distributions along azimuth direction.The incidence field mode can benefit
It is realized with existing spatial light modulation technology and newest super sufacing.
Demonstrating the same focal spot array of two dimension with special properties by above-described embodiment can be by the side without optimization
Formula building.Simultaneously by above-described embodiment it follows that there are one-to-one relationships between focal spot and dipole in (1) array；
(2) number of focal spots on focal plane is equal to the array element quantity in planar array antenna；(3) centre coordinate of each focal spot with it is corresponding
The coordinate of antenna element is identical；(4) adjacent focal spot along X-axis and Y-axis interval be only dependent upon corresponding two antenna elements X to and Y-direction
Interval.That is, the required same focal spot array of two dimension can be by inversely focusing the radiation of corresponding dipole array
Field is customized.The same focal spot array of two dimension that the present embodiment method generates has in terms of parallel processing many potentially answers
With, such as multiparticle accelerates parallel, multiparticle manipulates parallel and the manufacture of multiparticle parallel fabrication.
The foregoing is merely presently preferred embodiments of the present invention, all equivalent changes done according to scope of the present invention patent with
Modification, is all covered by the present invention.
Claims (4)
1. a kind of method that the radiation field using planar array antenna generates the same focal spot array of two dimension, it is characterised in that: including with
Lower step:
Step S1: 4 π focusing systems are formed using two high numerical aperture lens；
Step S2: at focal plane central array one of the 4 π focusing systems of step S1 being made of two high numerical aperture lens
Virtual planar array antenna；The electric field of antenna array radiationThe lens for reaching image space side are propagated outward, and by two
A high numerical aperture lens are collected completely, are then continued to travel on the pupil plane of two lens, be obtained on pupil plane
Field distributionWherein,It is spherical coordinates,It is the polar coordinates on pupil plane, θ indicates radiation direction and Z axis
Between angle,Indicate azimuth, ρ indicates polar diameter；
Step S3: by the field distribution on the pupil plane in step S2It is considered as in-field and is inversely transferred to Jiao Qu, in height
The same focal spot array of two dimension with predetermined properties is generated on the focal plane of lens numerical aperture.
2. the side that a kind of radiation field using planar array antenna according to claim 1 generates the same focal spot array of two dimension
Method, it is characterised in that: in step S2, the electric field of the antenna array radiationIt is indicated using following formula:
In formula, C0It is the coefficient unrelated with antenna pattern,It is the unit vector along the direction θ,It is first factor,It is array factor；For electric Hertz antenna unit,
Projection function g (θ) and apodizing function P (θ) for deferring to the lens of Helmholtz's condition, in spheric wave front are as follows:
G (θ)=tan θ；
The then field distribution on pupil planeIt is calculated by following formula:
In formula,Indicate azimuth,Indicate the unit vector of X-direction,Indicate the unit vector of Y direction.
3. the side that a kind of radiation field using planar array antenna according to claim 2 generates the same focal spot array of two dimension
Method, it is characterised in that: if planar array antenna is the M × N number of unit rectangle battle array arranged along X-axis and Y-axis, array factorIt indicates are as follows:
In formula, k=2 π/λ is wave number, dxAnd dyRow and column spacing of the adjacent element between X-axis and Y-axis is respectively represented, M is indicated
Along the element number of array of X-axis arrangement, N indicates the element number of array arranged along Y-axis；
If planar array antenna is circle made of circumferentially arranging, array factorIt indicates are as follows:
In formula, R indicates that the radius of circular array, Q indicate the element number of array circumferentially arranged,It is the azimuth of q-th of array element.
4. the side that a kind of radiation field using planar array antenna according to claim 1 generates the same focal spot array of two dimension
Method, it is characterised in that: the Field distribution of focal plane in step S3, on focal plane are as follows:
In formula,φ=cos-1(x/r), C1It is amplitude constant, Ex(r,φ,z)、Ey(r, φ, z) and Ez(r,φ,
Z) X, Y, Z-direction field component at point of observation on focal plane (r, φ, z=0) are illustrated respectively in.
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| CN112558297A (en) * | 2020-12-15 | 2021-03-26 | 泉州师范学院 | Method for generating optical needle focal field pointing to any space based on uniform line source radiation field |
| CN112946883A (en) * | 2021-02-26 | 2021-06-11 | 泉州师范学院 | Method for generating transverse optical needle planar array |
| CN112946882A (en) * | 2021-02-26 | 2021-06-11 | 泉州师范学院 | Method for generating light tube focal field with customizable space direction and length |
| CN112946881A (en) * | 2021-02-26 | 2021-06-11 | 泉州师范学院 | Method for generating arbitrary pointing light needle three-dimensional array |
| CN114114702A (en) * | 2021-12-06 | 2022-03-01 | 暨南大学 | Method for generating arbitrary orientation energy flow in sub-wavelength spatial scale |
| CN115291386A (en) * | 2022-10-10 | 2022-11-04 | 泉州师范学院 | Method for realizing random pointing of same light focal spot to linear array |
| CN117724244A (en) * | 2024-02-07 | 2024-03-19 | 泉州师范学院 | Method for constructing multi-degree-of-freedom height-controllable local light ring linear array focal field |
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| CN112558297A (en) * | 2020-12-15 | 2021-03-26 | 泉州师范学院 | Method for generating optical needle focal field pointing to any space based on uniform line source radiation field |
| CN112946883A (en) * | 2021-02-26 | 2021-06-11 | 泉州师范学院 | Method for generating transverse optical needle planar array |
| CN112946882A (en) * | 2021-02-26 | 2021-06-11 | 泉州师范学院 | Method for generating light tube focal field with customizable space direction and length |
| CN112946881A (en) * | 2021-02-26 | 2021-06-11 | 泉州师范学院 | Method for generating arbitrary pointing light needle three-dimensional array |
| CN112946881B (en) * | 2021-02-26 | 2022-10-14 | 泉州师范学院 | Method for generating arbitrary pointing light needle three-dimensional array |
| CN114114702A (en) * | 2021-12-06 | 2022-03-01 | 暨南大学 | Method for generating arbitrary orientation energy flow in sub-wavelength spatial scale |
| CN114114702B (en) * | 2021-12-06 | 2022-06-14 | 暨南大学 | Method for generating arbitrary orientation energy flow in sub-wavelength spatial scale |
| CN115291386A (en) * | 2022-10-10 | 2022-11-04 | 泉州师范学院 | Method for realizing random pointing of same light focal spot to linear array |
| CN115291386B (en) * | 2022-10-10 | 2023-02-24 | 泉州师范学院 | Method for realizing random pointing of same light focal spot to linear array |
| CN117724244A (en) * | 2024-02-07 | 2024-03-19 | 泉州师范学院 | Method for constructing multi-degree-of-freedom height-controllable local light ring linear array focal field |
| CN117724244B (en) * | 2024-02-07 | 2024-05-03 | 泉州师范学院 | Method for constructing multi-degree-of-freedom height-controllable local light ring linear array focal field |
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